Properties of acoustic plate modes (APMs) in YZ LiNbO₃ were calculated and measured. It was found that these modes have a dominant longitudinal component of mechanical motion concentrated near both surfaces of a plate. A delay line with double-electrode interdigital transducers (IDTs) was used for the measurements. Because of good matching to the load, strong triple-transit signals (TTS) were generated and insertion loss of about 7 dB was achieved at a frequency of about 131.4 MHz. Using water and glycerin solutions, insertion loss changes against viscosity were measured for this mode. In a viscosity range from about 1 mPa·s to 1000 mPa·s, an insertion loss change of about 16 dB was obtained. High sensitivity of viscosity measurement over a wide range makes the APMs in YZ LiNbO₃ attractive for application in viscosity sensors.